Today more than ever, electric utilities are faced with the challenges of optimization of their resources, reduction of operating costs, and delivery of power reliably to their customers. In addition, the utility sector has an aging workforce. There are a number of occupational situations in utility operations where decision-making relies heavily on experience and lack of this body of knowledge may lead to inferior decision-making and reduced reliability. An effective way to tackle these challenges is through utility automation and automated asset monitoring and decision making in particular.
In distribution systems, underground feeder maintenance and upkeep of medium voltage cables make up a significant chunk of operations and maintenance (O&M) expenditures. These cables may suffer from degradation over time due to various environmental, electrical, and mechanical factors. Deterioration of the assets gives rise to incipient faults that may be benign in the early stages but, over time, may lead to a catastrophic failure.
Deterioration of insulating materials typically conveys itself as sporadic arcing, which is believed to increase in severity as the equipment nears failure. Most often, the insulation material undergoes a gradual aging process before a catastrophic fault occurs. During this period, the electrical properties of the insulation alter adversely and incipient fault behavior commences. Incipient behavior is portrayed as a spike or series of spikes (burst) in the measured current waveforms. This is a direct result of an ongoing aging and deterioration process in the insulation medium used in power equipment, such as distribution cables and transformers. The abnormalities introduced by incipient behavior are indicators of system health. As the system ages, this atypical behavior tends to exhibit itself conspicuously. Persisting incipient abnormalities can eventually lead to a catastrophic failure and unscheduled outages.
Incipient faults convey intermittent, asymmetric, and sporadic spikes, which are random in magnitude and could involve sporadic bursts as well. They exhibit complex, nonlinear, and dynamic characteristics and may not last for a definite period. They may persist in the system from as little as several days to several years. Incipient faults do not typically draw sufficient current from the line to activate the protective devices. In addition, they may manifest themselves in the high frequency spectrum of the current signal.
In the past, the Laplace test statistic (LTS) was used as a simple but powerful tool for identifying the trend of an incipient failure from the recorded precursor events. This technique is popular in reliability studies and has been proposed for trend analysis in power systems for decision making regarding asset maintenance.
Traditional LTS uses the arrival times of incipient failure events as the only parameter for determining the statistical trend. This way, each event is treated equally in terms of its contribution to the eventual failure. But, consider a situation where one needs to monitor two parameters that are believed to contribute explicitly to the eventual failure. This requirement would not be fulfilled by the conventional trend analysis as it does not explicitly take any other parameter, apart from the arrival time, into consideration.
The Laplace Test Statistic applied to a series of chronologically ordered events explains the rate of arrival of the events in the observation window. The arrival times of N chronologically ordered events are shown, for example, in FIG. 1. When monitoring incipient failures, each recorded instance of an incipient failure is regarded as an event.
Let tN+1 be the time at which the fault occurred, N be the number of incipient failure events that occurred before the fault, and δ be the time between successive events. The LTS is given by (1):
                    LTS        =                                                            1                N                            ⁢                                                ∑                                      i                    =                    1                                    N                                ⁢                                                      ∑                                          j                      =                      1                                        i                                    ⁢                                      δ                    j                                                                        -                                          t                                  N                  +                  1                                                            2                ⁢                                                                                                                          t                              N                +                1                                      ·                                          1                                  12                  ⁢                  N                                                                                        (        1        )            WhereN=the number of incipient events recorded,δj=the inter-arrival times,ti=time at the ith sampleEquation (1) can be reduced to
                              LTS          =                                                                      1                  N                                ⁢                                                      ∑                                          i                      =                      1                                        N                                    ⁢                                      (                                                                  δ                        1                                            +                                              δ                        2                                            +                      …                      +                                              δ                        i                                                              )                                                              -                                                t                                      N                    +                    1                                                  2                                                                    t                                  N                  +                  1                                            ·                                                1                                      12                    ⁢                    N                                                                                      ⁢                                  ⁢                  And          ⁢                                          ⁢          further                                    (        2        )                                LTS        =                                                                              ∑                                      i                    =                    1                                    N                                ⁢                                  t                  i                                            N                        -                                          t                                  N                  +                  1                                            2                                                          t                              N                +                1                                      ·                                                            1                                      12                    ⁢                    N                                                  ⁢                                                                                                                          (        3        )            
Equation (3) defines the LTS in its most common form that is applied to a series of events in order to determine whether a statistical trend is present. The LTS behavior has a straightforward interpretation under different assumptions. Under the assumption that the events occur at a constant rate, δ would be a constant over the interval (t1,tN). Therefore, the mean of all ti's would be at the midpoint of the interval. Consequently, the LTS value would be very close to zero. However, if the rate of occurrence of events increases with time and becomes high near the end of the interval, the LTS value would be positive and large. Finally, if the events decrease near the end of the interval, the LTS value would be negative and small.
In practice, identifying a statistical trend of events is important for monitoring purposes but to use this information for prediction, the trend needs to be quantified and compared against a threshold for alarming purposes. An empirical upper bound for the LTS is:LTSmax≈√{square root over (3N)}  (4)
In practice the theoretical upper bound and may never be reached due to the intermittent on/off nature of incipient faults. Nevertheless, for practical purposes, a percentage of this theoretical upper bound may be used for setting an alarm threshold.
For on-line applications, a growing window of events (see FIG. 2) can be used for calculating the trend trajectory over time. In this case, more samples are added with increased number of incipient failure events and the resulting LTS values corresponding to each window are used for alarming purposes. Intuitively, the value of N would not be a constant. Therefore, according to equation (4), the threshold value would change with the increase in the window size. In such a case, the calculated LTS values would be compared against a dynamic threshold that is updated at each iteration.
Despite the above referenced advantages of LST applications, drawbacks persist. In particular, the LST methods above fail to adequately account for a plurality of parameters.